The 14-time major winner – on his first PGA Tour start in a year – finished the third day three under overall, eight behind leader Alex Noren, of Sweden.
Woods struggled off the tee, finding only three of 14 fairways, although he holed some crucial pressure putts.
“It was gross,” said the 42-year-old American, who has undergone four back operations since 2014.
Noren, a nine-time winner on the European Tour but yet to break his duck on the PGA equivalent, heads into the final round with a one-shot lead after a three-under 69.
Ryan Palmer sits on 10 under after a disappointing 73 on Saturday while fellow American JB Holmes has catapulted himself up the leaderboard after a 65 to sit just two off the lead.
Compatriot Michael Kim joins him on nine under, while England’s Justin Rose and former world number one Jason Day are two of seven players one shot further back.
Defending champion Jon Rahm, who was in second place, slipped to 12th with a 75, putting him seven under overall.
